Question: Find the intersection of the lines $9x-4y=6$ and $7x+y=17$. Express your answer as an ordered pair $(x,y)$.
We can find $x$ by taking four times the second equation plus the first:

$4(7x+y)+(9x-4y)=28x+9x=37x=4(17)+6=74\implies x=2$.

Substituting into the second equation, we can find $y$:

$7x+y=17\implies y=17-7x=17-7(2)=3$.

Thus our answer is $\boxed{(2,3)}$.